Solve the Inequality for h h<=(6h+3)/5

$h \leq \frac{6 h + 3}{5}$

Step 1

Multiply both sides by $5$ .

$h \cdot 5 \leq \frac{6 h + 3}{5} \cdot 5$

Step 2

Simplify.

Simplify the left side.

Move $5$ to the left of $h$ .

$5 h \leq \frac{6 h + 3}{5} \cdot 5$

Simplify the right side.

Simplify $\frac{6 h + 3}{5} \cdot 5$ .

Factor $3$ out of $6 h + 3$ .

Factor $3$ out of $6 h$ .

$5 h \leq \frac{3 (2 h) + 3}{5} \cdot 5$

Factor $3$ out of $3$ .

$5 h \leq \frac{3 (2 h) + 3 (1)}{5} \cdot 5$

Factor $3$ out of $3 (2 h) + 3 (1)$ .

$5 h \leq \frac{3 (2 h + 1)}{5} \cdot 5$

Cancel the common factor of $5$ .

Cancel the common factor.

$5 h \leq \frac{3 (2 h + 1)}{5} \cdot 5$

Rewrite the expression.

$5 h \leq 3 (2 h + 1)$

Apply the distributive property.

$5 h \leq 3 (2 h) + 3 \cdot 1$

Multiply.

Multiply $2$ by $3$ .

$5 h \leq 6 h + 3 \cdot 1$

Multiply $3$ by $1$ .

$5 h \leq 6 h + 3$

Step 3

Solve for $h$ .

Move all terms containing $h$ to the left side of the inequality.

Subtract $6 h$ from both sides of the inequality.

$5 h - 6 h \leq 3$

Subtract $6 h$ from $5 h$ .

$- h \leq 3$

Divide each term in $- h \leq 3$ by $- 1$ and simplify.

Divide each term in $- h \leq 3$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- h}{- 1} \geq \frac{3}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{h}{1} \geq \frac{3}{- 1}$

Divide $h$ by $1$ .

$h \geq \frac{3}{- 1}$

Simplify the right side.

Divide $3$ by $- 1$ .

$h \geq - 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$h \geq - 3$

Interval Notation:

$[- 3, \infty)$

Solve the Inequality for h h<=(6h+3)/5

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